Faculty ID Age Years of Service Rank School Gender M/F Salary ($/year) 1 49 22 A
ID: 3199028 • Letter: F
Question
Faculty ID Age Years of Service Rank School Gender M/F Salary ($/year) 1 49 22 ASST BUSINESS F 106632 2 31 0 ASST BUSINESS F 80000 3 34 2 ASST BUSINESS F 114666 4 34 0 ASST BUSINESS F 112000 5 41 6 ASSO BUSINESS F 119962 6 28 0 ASST BUSINESS F 110000 7 58 23 ASSO LIBERAL STUDIES F 94376 8 52 22 ASST LIBERAL STUDIES F 83506 9 35 6 ASSO LIBERAL STUDIES F 81124 10 37 7 ASSO LIBERAL STUDIES F 75116 11 42 7 ASSO LIBERAL STUDIES F 83568 12 30 3 ASST LIBERAL STUDIES F 66958 13 57 23 PROF LIBERAL STUDIES F 111758 14 53 23 PROF LIBERAL STUDIES F 110750 15 26 0 ASST LIBERAL STUDIES F 74000 16 59 30 ASST LIBERAL STUDIES F 98926 17 39 4 ASST LIBERAL STUDIES F 66190 18 51 19 ASSO LIBERAL STUDIES F 95138 19 38 4 ASST LIBERAL STUDIES F 66190 20 54 21 ASSO LIBERAL STUDIES F 84870 21 43 17 ASSO LIBERAL STUDIES F 78460 22 35 0 ASST LIBERAL STUDIES F 56700 23 31 3 ASST LIBERAL STUDIES F 63666 24 41 6 ASSO LIBERAL STUDIES F 76908 25 31 1 ASST LIBERAL STUDIES F 62776 26 56 21 PROF LIBERAL STUDIES F 105900 27 43 18 ASSO LIBERAL STUDIES F 90310 28 48 20 ASSO LIBERAL STUDIES F 92424 29 49 21 ASST HEALTH F 95386 30 49 17 ASSO HEALTH F 87098 31 40 7 ASSO HEALTH F 74218 32 32 1 ASST HEALTH F 64800 33 37 4 ASST HEALTH F 71314 34 54 24 PROF HEALTH F 110770 35 32 3 ASST HEALTH F 66924 36 38 7 ASSO HEALTH F 74410 37 34 6 ASST HEALTH F 65700 38 28 3 ASST HEALTH F 70218 39 26 1 ASST HEALTH F 76900 40 35 2 ASST HEALTH F 70210 41 33 2 ASST HEALTH F 71088 42 40 8 ASSO SCIENCES F 78484 43 35 1 ASST SCIENCES F 66906 44 36 3 ASST SCIENCES F 69112 45 32 3 ASST SCIENCES F 71088 46 29 2 ASST SCIENCES F 73180 47 43 12 ASST SCIENCES F 82330 48 37 5 ASST SCIENCES F 70210 49 34 7 ASSO SCIENCES F 81432 50 34 8 ASST SCIENCES F 73332 51 35 9 ASST SCIENCES F 67200 52 41 6 ASST SCIENCES F 67328 53 39 11 ASST SCIENCES F 79646 54 44 17 ASSO SCIENCES F 98104 55 46 12 ASST SCIENCES F 73154 56 42 11 ASST SCIENCES F 68878 57 36 1 ASSO SCIENCES F 81000 58 43 18 ASST SCIENCES F 82190 59 51 19 ASST SCIENCES F 81286 60 51 16 ASSO SCIENCES F 87940 61 54 19 ASST SCIENCES F 85498 62 45 10 ASST SCIENCES F 72406 63 38 11 ASSO SCIENCES F 85848 64 39 8 ASST SCIENCES F 74332 65 50 19 ASST SCIENCES F 83946 66 33 2 ASST SCIENCES F 73180 67 44 11 PROF BUSINESS M 128750 68 37 7 ASSO BUSINESS M 127002 69 37 6 ASSO BUSINESS M 118852 70 45 20 ASSO BUSINESS M 98116 71 34 4 PROF BUSINESS M 189938 72 47 21 ASST BUSINESS M 109524 73 36 9 ASSO BUSINESS M 111032 74 44 18 ASSO BUSINESS M 91864 75 40 11 ASSO BUSINESS M 113742 76 31 5 ASST BUSINESS M 121770 77 29 2 PROF BUSINESS M 167266 78 37 2 ASST BUSINESS M 116000 79 40 14 ASST BUSINESS M 82550 80 44 10 PROF BUSINESS M 127282 81 45 17 ASST BUSINESS M 100212 82 33 7 ASSO BUSINESS M 116100 83 35 3 ASSO BUSINESS M 138842 84 49 22 ASSO BUSINESS M 115500 85 36 9 ASSO BUSINESS M 112988 86 32 6 PROF BUSINESS M 156614 87 33 5 PROF BUSINESS M 147728 88 59 24 ASSO LIBERAL STUDIES M 102856 89 47 21 ASSO LIBERAL STUDIES M 91430 90 59 27 PROF LIBERAL STUDIES M 112144 91 40 12 ASST LIBERAL STUDIES M 75096 92 47 14 PROF LIBERAL STUDIES M 102144 93 27 0 ASSO LIBERAL STUDIES M 78000 94 37 8 ASST LIBERAL STUDIES M 81016 95 41 16 ASST LIBERAL STUDIES M 74374 96 41 7 ASSO LIBERAL STUDIES M 103774 97 57 22 ASST LIBERAL STUDIES M 92682 98 29 0 ASST LIBERAL STUDIES M 65812 99 61 30 PROF LIBERAL STUDIES M 118512 100 59 24 PROF LIBERAL STUDIES M 119286 101 53 25 PROF LIBERAL STUDIES M 138838 102 54 19 ASSO LIBERAL STUDIES M 88126 103 47 22 PROF LIBERAL STUDIES M 112918 104 40 8 ASSO LIBERAL STUDIES M 80000 105 50 23 PROF LIBERAL STUDIES M 112008 106 36 7 ASSO LIBERAL STUDIES M 72828 107 51 18 PROF LIBERAL STUDIES M 94240 108 55 25 ASSO LIBERAL STUDIES M 99262 109 41 11 PROF LIBERAL STUDIES M 91164 110 59 24 PROF LIBERAL STUDIES M 110330 111 57 24 PROF LIBERAL STUDIES M 115032 112 55 22 ASSO LIBERAL STUDIES M 94506 113 27 0 ASST LIBERAL STUDIES M 63000 114 37 7 ASSO LIBERAL STUDIES M 75922 115 53 22 PROF LIBERAL STUDIES M 116014 116 34 0 ASST LIBERAL STUDIES M 63000 117 37 12 ASSO LIBERAL STUDIES M 83714 118 27 2 ASST LIBERAL STUDIES M 64892 119 30 0 ASST LIBERAL STUDIES M 63000 120 58 24 PROF LIBERAL STUDIES M 116878 121 58 25 PROF LIBERAL STUDIES M 140036 122 47 20 ASSO LIBERAL STUDIES M 93688 123 36 11 PROF LIBERAL STUDIES M 130566 124 33 8 ASSO LIBERAL STUDIES M 73170 125 62 28 ASSO LIBERAL STUDIES M 112672 126 35 6 ASSO LIBERAL STUDIES M 71940 127 49 21 PROF LIBERAL STUDIES M 105308 128 49 24 PROF LIBERAL STUDIES M 108416 129 59 25 PROF LIBERAL STUDIES M 112510 130 41 16 PROF LIBERAL STUDIES M 93914 131 39 8 ASSO LIBERAL STUDIES M 80002 132 46 16 ASSO LIBERAL STUDIES M 87362 133 32 7 ASSO LIBERAL STUDIES M 81968 134 53 25 PROF LIBERAL STUDIES M 134086 135 51 22 PROF LIBERAL STUDIES M 131962 136 57 25 PROF LIBERAL STUDIES M 108328 137 50 18 ASST LIBERAL STUDIES M 76948 138 59 24 PROF LIBERAL STUDIES M 116882 139 48 22 ASSO LIBERAL STUDIES M 98082 140 46 17 ASST LIBERAL STUDIES M 79104 141 50 23 ASSO LIBERAL STUDIES M 95618 142 56 25 PROF LIBERAL STUDIES M 114312 143 34 1 ASST HEALTH M 70876 144 48 20 ASSO HEALTH M 94694 145 53 20 PROF HEALTH M 108514 146 33 8 ASSO HEALTH M 95546 147 56 23 PROF HEALTH M 127950 148 30 1 ASST HEALTH M 70876 149 47 16 PROF HEALTH M 109672 150 34 7 ASST HEALTH M 71776 151 55 20 PROF HEALTH M 98176 152 55 23 PROF HEALTH M 131104 153 51 22 ASST HEALTH M 90222 154 51 23 ASSO HEALTH M 112980 155 33 2 PROF HEALTH M 216676 156 54 26 ASST HEALTH M 111170 157 37 2 ASST HEALTH M 73988 158 53 21 ASSO HEALTH M 113858 159 53 21 ASSO HEALTH M 93740 160 46 17 ASSO HEALTH M 92314 161 31 2 ASST SCIENCES M 68998 162 28 0 ASST SCIENCES M 70400 163 58 24 PROF SCIENCES M 107188 164 34 8 ASSO SCIENCES M 80462 165 43 8 ASSO SCIENCES M 74336 166 32 6 ASST SCIENCES M 68016 167 42 17 PROF SCIENCES M 96036 168 30 3 ASST SCIENCES M 76796 169 52 18 PROF SCIENCES M 106422 170 63 28 PROF SCIENCES M 137980 171 37 2 ASST SCIENCES M 70880 172 55 25 PROF SCIENCES M 116100 173 27 0 ASST SCIENCES M 68000 174 59 26 PROF SCIENCES M 126018 175 43 9 ASSO SCIENCES M 82836 176 50 21 PROF SCIENCES M 101558 177 61 29 PROF SCIENCES M 131302 178 55 23 ASSO SCIENCES M 107222 179 67 41 ASSO SCIENCES M 115342 180 34 6 ASSO SCIENCES M 84418 181 50 21 PROF SCIENCES M 93946 182 55 23 PROF SCIENCES M 110138 183 43 8 ASSO SCIENCES M 74478 184 53 25 ASSO SCIENCES M 102814 185 44 13 PROF SCIENCES M 119386 186 33 0 ASST SCIENCES M 69000 187 43 12 ASST SCIENCES M 82266 188 37 4 ASST SCIENCES M 71088 189 43 14 ASST SCIENCES M 78240 190 47 14 ASST SCIENCES M 89808 191 55 22 PROF SCIENCES M 108284 192 40 9 ASST SCIENCES M 100324 193 48 22 ASSO SCIENCES M 125832 194 47 14 PROF SCIENCES M 107322 195 41 12 PROF SCIENCES M 94672 196 49 14 PROF SCIENCES M 89460 197 37 11 ASSO SCIENCES M 84378 198 36 10 ASST SCIENCES M 72406 199 42 14 ASSO SCIENCES M 91458 You conduct a stepwise regression according to the following procedure Step 1: Gender ony Step 2: Gender and School Step 3 Gender, School and Rank Step 4: Gender, School, Rank and Years of Service Step 5: Gender, School, Rank, Years of Service and Age Choice of reference variable: it is recommended that you choose Health and ASSO as the reference variables for the cotegorical variables: School and Rank. Present the regression output for each of the five steps 4 marks) 5. Based on the regression output obtained in Step 4, answer the following (a) Which summary measure in the regression output is used to assess the overall adequacy of the model? Comment on the overall adequacy of the model obtained in Step 4 (2 marks) (b) For eoch of the four independent variables, fully interpret the regression coefficients and comment on their statistical significance. (In discussing statistical significance of a regression (6 marks] Based on the correlation between Age and Salary, did you expect Age to have a statistically coefficient, you have to justify your choice of one or two toil test.) 6. significant effect on Salary? In Step 5, is the statistical significance of the regression coefficient of Age as expected? Discuss fully. (3 marks)Explanation / Answer
Solution for problem 4.
Given,
Step 1: Gender only
Step 2: Gender and School
Step 3 Gender, School and Rank
Step 4: Gender, School, Rank and Years of Service
Step 5: Gender, School, Rank, Years of Service and Age
Code:
> data1=read.csv(file.choose(),header=T)
> fulldata=data1[,-1] #removing the ID variable
> attach(fulldata)
The following objects are masked from data1 (pos = 3):
Age, Gender, Rank, Salary, School, Years
> names(fulldata)
[1] "Age" "Years" "Rank" "School" "Gender" "Salary"
> Rank=relevel(Rank,ref="ASSO") #releveling the variable and changing the reference
> School=relevel(School,ref="HEALTH")
> null=lm(Salary~Gender,data=fulldata) # base model
> null
Call:
lm(formula = Salary ~ Gender, data = fulldata)
Coefficients:
(Intercept) GenderM
81665 19471
> full=lm(Salary~.,data=fulldata) #upper model
> full
Call:
lm(formula = Salary ~ ., data = fulldata)
Coefficients:
(Intercept) Age Years RankASST RankPROF SchoolHEALTH SchoolLIBERAL STUDIES
108235.95 72.63 521.95 -10153.40 23431.59 -26979.21 -35038.58
SchoolSCIENCES GenderM
-33177.18 3538.51
> step(null, scope=list(lower=null, upper=full), direction="forward") #stepwise regression
Start: AIC=3988.13
Salary ~ Gender
Df Sum of Sq RSS AIC
+ Rank 2 3.8321e+10 6.0252e+10 3894.2
+ School 3 1.7597e+10 8.0976e+10 3955.0
+ Years 1 1.3254e+10 8.5319e+10 3961.4
+ Age 1 1.3039e+10 8.5534e+10 3961.9
<none> 9.8573e+10 3988.1
Step: AIC=3894.17
Salary ~ Gender + Rank
Df Sum of Sq RSS AIC
+ School 3 2.1779e+10 3.8473e+10 3810.9
+ Years 1 6.9627e+08 5.9556e+10 3893.9
<none> 6.0252e+10 3894.2
+ Age 1 3.6399e+08 5.9888e+10 3895.0
Step: AIC=3810.91
Salary ~ Gender + Rank + School
Df Sum of Sq RSS AIC
+ Years 1 3.774e+09 3.4700e+10 3792.4
+ Age 1 3.329e+09 3.5145e+10 3794.9
<none> 3.8473e+10 3810.9
Step: AIC=3792.36
Salary ~ Gender + Rank + School + Years
Df Sum of Sq RSS AIC
<none> 3.4700e+10 3792.4
+ Age 1 10147983 3.4689e+10 3794.3
Call:
lm(formula = Salary ~ Gender + Rank + School + Years, data = fulldata)
Coefficients:
(Intercept) GenderM RankASST RankPROF SchoolHEALTH SchoolLIBERAL STUDIES SchoolSCIENCES
110407.4 3450.3 -10169.2 23551.6 -26906.4 -34974.8 -33083.5
Years
593.6
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